Heat conduction worksheet with answers

Free printable Heat conduction worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
Concrete, k = 1.450 mm25 °C-13 °CQ̇ = ?

A wall of concrete is 50 mm thick and has an area of 6 m². Its faces are held at 25 °C and -13 °C. Find the rate of heat conduction Q̇ through the wall.

k = 1.4 W/(m·K)L = 50 mmA = 6 m²T1 = 25 °CT2 = -13 °C
Q̇ = W
2.Easy
Glass, k = 0.96100 mm16 °C-5 °CQ̇ = ?

A wall of glass is 100 mm thick and has an area of 8 m². Its faces are held at 16 °C and -5 °C. Find the rate of heat conduction Q̇ through the wall.

k = 0.96 W/(m·K)L = 100 mmA = 8 m²T1 = 16 °CT2 = -5 °C
Q̇ = W
3.Medium
Glass, k = 0.96150 mmWood, k = 0.1775 mm19 °C-12 °CTi​ = ?Q̇

A wall is made of 150 mm of glass and 75 mm of wood, with an area of 6 m². The outer faces are at 19 °C and -12 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.96 W/(m·K)L2 = 75 mm, k2 = 0.17 W/(m·K)A = 6 m²T1 = 19 °CT3 = -12 °C
Ti = °C
4.Medium
Gypsum board, k = 0.17150 mmMineral wool, k = 0.0425 mm23 °C-4 °CTi​ = ?Q̇

A wall is made of 150 mm of gypsum board and 25 mm of mineral wool, with an area of 15 m². The outer faces are at 23 °C and -4 °C. Find the temperature Ti at the interface between the two layers.

L1 = 150 mm, k1 = 0.17 W/(m·K)L2 = 25 mm, k2 = 0.04 W/(m·K)A = 15 m²T1 = 23 °CT3 = -4 °C
Ti = °C
5.Hard
Mineral wool, k = 0.04250 mmWood, k = 0.17150 mmroom 22 °Coutside -3 °CQ̇

A wall of 250 mm mineral wool and 150 mm wood separates a room at 22 °C from outside air at -3 °C. The convection coefficients are 6 W/(m²·K) inside and 20 W/(m²·K) outside, and the wall area is 4 m². Find the overall heat transfer coefficient U of the wall.

L1 = 250 mm, k1 = 0.04 W/(m·K)L2 = 150 mm, k2 = 0.17 W/(m·K)A = 4 m²hi = 6 W/(m²·K)ho = 20 W/(m²·K)Troom = 22 °CTout = -3 °C
U = W/(m²·K)
6.Hard
Expanded polystyrene, k = 0.035100 mmGlass, k = 0.96150 mmroom 22 °Coutside 2 °CQ̇ = ?

A wall of 100 mm expanded polystyrene and 150 mm glass separates a room at 22 °C from outside air at 2 °C. The convection coefficients are 10 W/(m²·K) inside and 30 W/(m²·K) outside, and the wall area is 15 m². Find the heat loss Q̇ through the wall.

L1 = 100 mm, k1 = 0.035 W/(m·K)L2 = 150 mm, k2 = 0.96 W/(m·K)A = 15 m²hi = 10 W/(m²·K)ho = 30 W/(m²·K)Troom = 22 °CTout = 2 °C
Q̇ = W

Answer key

  1. 1. Q̇ = 6384 W
  2. 2. Q̇ = 1613 W
  3. 3. Ti = 10.89 °C
  4. 4. Ti = 7.195 °C
  5. 5. U = 0.1361 W/(m²·K)
  6. 6. Q̇ = 95.34 W

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